From a357181b71bee000723d57abec2cfb796a6e4836 Mon Sep 17 00:00:00 2001
From: Fredrik Johansson <fredrik.johansson@gmail.com>
Date: Wed, 7 Sep 2016 16:25:32 +0200
Subject: [PATCH] add polynomial valuation functions

---
 acb_poly.h              |  2 ++
 acb_poly/valuation.c    | 25 +++++++++++++++++++++++++
 arb_poly.h              |  2 ++
 arb_poly/valuation.c    | 25 +++++++++++++++++++++++++
 doc/source/acb_poly.rst |  5 +++++
 doc/source/arb_poly.rst |  5 +++++
 6 files changed, 64 insertions(+)
 create mode 100644 acb_poly/valuation.c
 create mode 100644 arb_poly/valuation.c

diff --git a/acb_poly.h b/acb_poly.h
index 0b1cd0ec..03d4140e 100644
--- a/acb_poly.h
+++ b/acb_poly.h
@@ -69,6 +69,8 @@ ACB_POLY_INLINE slong acb_poly_degree(const acb_poly_t poly)
     return poly->length - 1;
 }
 
+slong acb_poly_valuation(const acb_poly_t poly);
+
 ACB_POLY_INLINE int
 acb_poly_is_zero(const acb_poly_t z)
 {
diff --git a/acb_poly/valuation.c b/acb_poly/valuation.c
new file mode 100644
index 00000000..76872387
--- /dev/null
+++ b/acb_poly/valuation.c
@@ -0,0 +1,25 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+slong
+acb_poly_valuation(const acb_poly_t poly)
+{
+    slong i, len = poly->length;
+
+    for (i = 0; i < len; i++)
+        if (!acb_is_zero(poly->coeffs + i))
+            return i;
+
+    return -1;
+}
+
diff --git a/arb_poly.h b/arb_poly.h
index 64b738b2..8002f59c 100644
--- a/arb_poly.h
+++ b/arb_poly.h
@@ -81,6 +81,8 @@ ARB_POLY_INLINE slong arb_poly_degree(const arb_poly_t poly)
     return poly->length - 1;
 }
 
+slong arb_poly_valuation(const arb_poly_t poly);
+
 ARB_POLY_INLINE int
 arb_poly_is_zero(const arb_poly_t z)
 {
diff --git a/arb_poly/valuation.c b/arb_poly/valuation.c
new file mode 100644
index 00000000..509feca2
--- /dev/null
+++ b/arb_poly/valuation.c
@@ -0,0 +1,25 @@
+/*
+    Copyright (C) 2016 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "arb_poly.h"
+
+slong
+arb_poly_valuation(const arb_poly_t poly)
+{
+    slong i, len = poly->length;
+
+    for (i = 0; i < len; i++)
+        if (!arb_is_zero(poly->coeffs + i))
+            return i;
+
+    return -1;
+}
+
diff --git a/doc/source/acb_poly.rst b/doc/source/acb_poly.rst
index 5ad90343..a4792017 100644
--- a/doc/source/acb_poly.rst
+++ b/doc/source/acb_poly.rst
@@ -143,6 +143,11 @@ Basic properties and manipulation
     Truncates *poly* to have length at most *n*, i.e. degree
     strictly smaller than *n*.
 
+.. function:: slong acb_poly_valuation(const acb_poly_t poly)
+
+    Returns the degree of the lowest term that is not exactly zero in *poly*.
+    Returns -1 if *poly* is the zero polynomial.
+
 Input and output
 -------------------------------------------------------------------------------
 
diff --git a/doc/source/arb_poly.rst b/doc/source/arb_poly.rst
index 4b7a1df5..0388b192 100644
--- a/doc/source/arb_poly.rst
+++ b/doc/source/arb_poly.rst
@@ -137,6 +137,11 @@ Basic manipulation
     Truncates *poly* to have length at most *n*, i.e. degree
     strictly smaller than *n*.
 
+.. function:: slong arb_poly_valuation(const arb_poly_t poly)
+
+    Returns the degree of the lowest term that is not exactly zero in *poly*.
+    Returns -1 if *poly* is the zero polynomial.
+
 Conversions
 -------------------------------------------------------------------------------